diadie scales

A long time ago, Gene wrote..

>It occurred to me that all of the notes of a comma pump, tempered by
>the comma in question, could make an interesting scale. I found ten
>scales, each of twelve notes, which support a 225/224 comma pump of
>tetrads such that each tetrad in the chord progression shares an
>interval with adjoining tetrads.
>//
>Moreover, we also have pentads; diadie2=pump9 gives us
>four pentads, two of each kind. More than the fact that it is a Fokker
>block, this leads me to regard it as the most interesting of these ten
>scales. Despite Carl's advocacy of diadie1, I think this also gives it
>the nod as the most interesting of the diadie blocks as well.

>I made a triad circle (around the circle of fifths) for the two
>diadieorw scales, but neglected to include them. Here they are.
>
>Diadieorw1 triad circle
>
>-5 [385.714286, 314.285714, 700.0000000]
>-4 [385.714286, 271.4285714, 657.1428571]
>-3 [428.5714286, 271.4285714, 700.0000000]
>-2 [428.5714286, 300.0000000, 728.5714286]
>-1 [385.7142854, 314.2857143, 700.0000000]
>0 [385.714286, 314.2857143, 700.0000000]
>1 [385.714286, 314.2857143, 700.0000000]
>2 [385.714286, 300.0000000, 685.7142857]
>3 [428.5714286, 271.4285714, 700.0000000]
>4 [428.5714286, 271.4285717, 700.0000000]
>5 [385.714286, 314.2857143, 700.0000000]
>6 [385.714286, 342.8571429, 728.5714286]
>
>I count five excellent 84-et major triads, one weird flat one,
>and three supermajor triads.
>
>Diadieorw2 triad circle
>
>-5 [385.714286, 314.285714, 700.000000]
>-4 [385.714286, 314.2857143, 700.0000000]
>-3 [385.714286, 271.4285714, 657.1428571]
>-2 [428.5714286, 300.0000000, 728.5714286]
>-1 [428.5714283, 271.4285714, 700.0000000]
>0 [385.714286, 314.2857143, 700.0000000]
>1 [385.714286, 314.2857143, 700.0000000]
>2 [385.714286, 342.8571429, 728.5714286]
>3 [385.714286, 271.4285714, 657.1428571]
>4 [428.5714286, 271.4285717, 700.0000000]
>5 [428.5714286, 271.4285714, 700.0000000]
>6 [385.714286, 342.8571429, 728.5714286]
>
>Four 84-et major triads, three supermajor triads.

Don't these triads circles reinforce an advocacy of diadie1?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Don't these triads circles reinforce an advocacy of diadie1?

Why do you say that?

>> Don't these triads circles reinforce an advocacy of diadie1?
>
>Why do you say that?

It has 10, as opposed to 8, triads.

-Carl

>>Diadieorw1 triad circle
>>
>>-5 [385.714286, 314.285714, 700.0000000]
>>-4 [385.714286, 271.4285714, 657.1428571]
>>-3 [428.5714286, 271.4285714, 700.0000000]
>>-2 [428.5714286, 300.0000000, 728.5714286]
>>-1 [385.7142854, 314.2857143, 700.0000000]
>>0 [385.714286, 314.2857143, 700.0000000]
>>1 [385.714286, 314.2857143, 700.0000000]
>>2 [385.714286, 300.0000000, 685.7142857]
>>3 [428.5714286, 271.4285714, 700.0000000]
>>4 [428.5714286, 271.4285717, 700.0000000]
>>5 [385.714286, 314.2857143, 700.0000000]
>>6 [385.714286, 342.8571429, 728.5714286]
>>
>>I count five excellent 84-et major triads, one weird flat one,
>>and three supermajor triads.
>>
>>Diadieorw2 triad circle
>>
>>-5 [385.714286, 314.285714, 700.000000]
>>-4 [385.714286, 314.2857143, 700.0000000]
>>-3 [385.714286, 271.4285714, 657.1428571]
>>-2 [428.5714286, 300.0000000, 728.5714286]
>>-1 [428.5714283, 271.4285714, 700.0000000]
>>0 [385.714286, 314.2857143, 700.0000000]
>>1 [385.714286, 314.2857143, 700.0000000]
>>2 [385.714286, 342.8571429, 728.5714286]
>>3 [385.714286, 271.4285714, 657.1428571]
>>4 [428.5714286, 271.4285717, 700.0000000]
>>5 [428.5714286, 271.4285714, 700.0000000]
>>6 [385.714286, 342.8571429, 728.5714286]
>>
>>Four 84-et major triads, three supermajor triads.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Don't these triads circles reinforce an advocacy of diadie1?
> >
> >Why do you say that?
>
> It has 10, as opposed to 8, triads.

Depends on what counts as a triad, I suppose.